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#1 Veggie boxes in pea gravel under tree
#2 Flat Shade Sail option
#3 Simple Plantings around patio to soften hardscape
#4 This has a few elements that remind me of your yard- I like how they added the narrow planters along the lawn to separate the grass from other areas. Adds a simple, clean border and the chance to add a few more textures and colors.
#5 Vertical water feature idea- can do something like this that is self contained vs having to build a pond underneath it.
#6 Basalt pillars are another good vertical water feature for a tight space. Just depends on the style you are looking for.